The On-Line Encyclopedia of Integer Sequences (OEIS)

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A275047

Diagonal of the rational function 1/(1-(1+w)(xy + xz + yz)) [even-indexed terms only].
(history; published version)

#29 by Andrey Zabolotskiy at Tue Nov 23 06:01:47 EST 2021

PROG

(PARI)

STATUS

approved

editing

#28 by Bruno Berselli at Thu Sep 23 03:56:16 EDT 2021

STATUS

reviewed

approved

#27 by Vaclav Kotesovec at Thu Sep 23 02:49:23 EDT 2021

STATUS

proposed

reviewed

#26 by Michel Marcus at Wed Sep 22 17:09:08 EDT 2021

STATUS

editing

proposed

#25 by Michel Marcus at Wed Sep 22 17:09:04 EDT 2021

LINKS

A. Bostan, S. Boukraa, J.-M. Maillard, and J.-A. Weil, <a href="http://arxiv.org/abs/1507.03227">Diagonals of rational functions and selected differential Galois groups</a>, arXiv preprint arXiv:1507.03227 [math-ph], 2015.

STATUS

proposed

editing

#24 by Peter Bala at Wed Sep 22 17:07:42 EDT 2021

STATUS

editing

proposed

#23 by Peter Bala at Mon Sep 20 07:28:09 EDT 2021

FORMULA

From Peter Bala, Sep 20 2021: (Start)

a(n) = 9*(3*n - 1)^2*(3*n - 2)^2/(2*n^3*(2*n - 1))*a(n-1).

a(n) = Sum_{k = n..3*n} (-1)^k*binomial(3*n,k)^2*binomial(k,n)^2. (End)

KEYWORD

nonn,easy

STATUS

approved

editing

#22 by Jon E. Schoenfield at Sat Dec 10 22:10:38 EST 2016

STATUS

editing

approved

#21 by Jon E. Schoenfield at Sat Dec 10 22:10:36 EST 2016

NAME

Diagonal of the rational function 1/(1-(1+w)(xy + xz + yz)) [even -indexed terms only].

COMMENTS

Odd -order terms are zero since R(x,y,z,w) = R(-x,-y,-z,w), where R(x,y,z,w) = 1/(1-(1+w)*(x*y + x*z + y*z)).

STATUS

approved

editing

#20 by N. J. A. Sloane at Sun Aug 07 22:28:59 EDT 2016

STATUS

proposed

approved